Hostname: page-component-7dd5485656-frp75 Total loading time: 0 Render date: 2025-10-31T01:45:04.221Z Has data issue: false hasContentIssue false
  • English
  • Français

The inviscid instability of a Blasius boundary layer at large values of the Mach number

Published online by Cambridge University Press:  26 April 2006

F. T. Smith  and
S. N. Brown
F. T. Smith
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
S. N. Brown
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

The unstable and neutral modes of a compressible boundary-layer flow past an insulated flat plate are discussed in the limit of infinite Mach number. These modes have been documented by Mack and many of the asymptotic results derived here are becoming evident in his computations at finite values of the Mach number. Of particular interest is the existence of a vorticity mode for which the wavenumber is a discontinuous function of Mach number at finite Mach number but is continuous in the limit M∞ → ∞. At large Mach number this is the most unstable mode, and is expected to have relevance also in the hypersonic limit when the flow field is no longer shock-free.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 219 , October 1990 , pp. 499 - 518
Copyright
© 1990 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Balsa, T. F. & Goldstein, M., 1990 On the instabilities of supersonic mixing layers: a high Mach number asymptotic theory. J. Fluid Mech. 216, 585–611.Google Scholar
Brown, S. N., Khorrami, A. F., Neish, A. & Smith, F. T., 1990 On hypersonic boundary-layer interactions and transition. Phil. Trans. R. Soc. (to appear).Google Scholar
Cowley, S. J. & Hall, P., 1990 On the instability of hypersonic flow past a wedge. J. Fluid Mech. 214, 17–42.Google Scholar
Jackson, T. L. & Grosch, C. E., 1989 Inviscid spatial stability of a compressible mixing layer. J. Fluid Mech. 208, 609–637.Google Scholar
Lees, L.: 1947 The stability of the laminar boundary layer in a compressible fluid. NACA Tech. Rep. 876.Google Scholar
Lees, L. & Lin, C. C., 1946 Investigation of the stability of the laminar boundary layer in a compressible fluid. NACA Tech. Note 1115.Google Scholar
Mack, L. M.: 1965 Computation of the stability of the laminar boundary layer. In Methods of Computational Physics (ed. B. Alder, S. Fernbach & M. Rotenberg), vol. 4, pp. 247–299. Academic.
Mack, L. M.: 1984 Boundary-layer linear stability theory. In Special Course on Stability and Transition of Laminar Flow. AGARD Rep. 709.
Mack, L. M.: 1987 Review of linear compressible stability theory. In Stability of Time Dependent and Spatially Varying Flows (ed. D. L. Dwoyer & M. Y. Hussaini). pp. 164–187. Springer.
Mack, L. M.: 1989 On the inviscid acoustic-mode instability of supersonic shear flows. Paper presented at Conference on Numerical and Physical Aspects of Aerodynamic Flows. Long Beach, CA.Google Scholar
Smith, F. T.: 1989 On the first-mode instability in subsonic, supersonic or hypersonic boundary layers. J. Fluid Mech. 198, 127–153.Google Scholar
Stewartson, K.: 1964 The Theory of Boundary Layers in Compressible Fluids. Oxford University Press.